Customizing the stiffness of a golf club shaft to perfectly suit a particular swing
will not increase clubhead speed (and therefore ball speed) enough to have any
meaningful effect on performance. This statement is confirmed by the clubhead speed
results generated from the simulations (Table 3.1.2.1). No single shaft stiffness out
performed the other two at any level of swing speed. At any given level of swing speed,
the difference in clubhead speeds across levels of shaft stiffness did not exceed 0.1 m/s.
An attempt was made to fine tune shaft stiffness even further by matching all possible
levels of shaft stiffness with a single swing. The results indicated that regardless of
Unfortunately, the marginal increases in clubhead speed were also accompanied by
unacceptable configurations of the golfer-club models at impact.
Previous studies have shown that shaft flexibility can increase clubhead speed
via the contribution from kick velocity (Butler & Winfield, 1994; Miao et al., 1998).
Even in this thesis, a kick velocity of 10.51 m/s (Table 3.1.2.1) at impact was recorded
for Golfer-Fast with Club-Regular suggesting that clubhead speed at impact would have
been reduced by 10.51 m/s if the shaft were perfectly rigid. Yet when Golfer-Fast was
matched with Club-Rigid, clubhead speed was only reduced by 1.87 m/s in comparison
to Club-Regular. Also, kick velocities at impact for Golfer-Fast/Club-Flexible (10.51
m/s) and Golfer-Fast/Club-Stiff (9.55 m/s) differed by approximately 1 m/s, yet both
simulations resulted in the same clubhead speed of 52.94 m/s at impact (Table 3.1.2.1).
These findings show that kick-velocity is a misleading variable. An understanding of
how kick velocity is produced is provided in the following paragraph and will explain
why kick velocity does not simply add on to the clubhead speed generating capabilities
of the golfer.
In an attempt to square the clubface for impact, tangential forces were applied at
the grip end of the club just past the halfway point into the downswing. This resulted in
the clubhead being deflected into a lagging position and the consequent storage of
energy in the rotational springs joining the shaft segments. This storage of energy was
accompanied by the rotational springs generating torques that tended to prevent
deflection in the lag direction and support deflection in the lead direction. As impact
approached, the tangential forces causing the lag deflection decreased which allowed the
leading position. This could also be referred to as the release of strain energy and was
facilitated by the action of radial force which was approaching its maximum value near
impact. This process certainly increased clubhead speed relative to the most proximal
club segment. Yet, it also served to simultaneously impede the absolute angular
velocity of the most proximal club segment which was a detriment to clubhead speed.
This happened because at the same time the restoring torque of the deformed rotational
spring served to increase the angular velocity of the distal segment, an equal and
opposite torque served to decrease the angular velocity of the proximal segment.
However, the golfer model did have some ability to oppose the decrease in angular
velocity of the most proximal club segment based on the properties of the muscle torque
generators. This is evident when comparing the clubhead speeds attained with the rigid
and non-rigid clubs (Table 3.2.1.1). Since clubhead speeds were greater with the non-
rigid clubs, it shows that the shaft did have some ability to store and release energy
during the swing. However, when comparing the non-rigid clubs, no particular level of
shaft stiffness had a superior ability to increase clubhead speed, through the contribution
of kick velocity, during the simulated swings (Table 3.1.2.1).
A golfer does not have the ability to produce constant levels of acceleration
during the downswing which has important implications when considering the potential
contribution from kick velocity. Researchers have developed golfer models which
employed fixed levels of acceleration during the downswing in an attempt study shaft
flexibility (Jorgensen, 1994; Miao et al., 1998). This is not a reasonable assumption
since the golfer model must be able to interact with the dynamic properties of the club.
generators, then the importance of shaft flexibility in contributing to clubhead speed
would have been greatly over estimated. If the angular acceleration of the most
proximal club segment was predetermined, then the torque from the rotational springs
would only serve to increase clubhead speed and not decrease the angular velocity of the
most proximal club segment. This would result in spuriously large clubhead speeds. It
is also likely that golfer robots may suffer from this same limitation; namely, the
inability to dynamically interact with the properties of a golf club in the same way as a
live golfer.
Currently, no researcher has presented conclusive results showing that different
shaft flexibilities result in measurably higher clubhead speeds at impact and therefore,
subsequently higher ball speeds. Miao et al. (1998) presented data which suggested that
certain levels of shaft stiffness resulted in higher clubhead speeds for a particular golfer.
However, as previously indicated in this thesis, it appears as though the error levels
associated with the data presented by Miao et al. were greater then the differences that
were measured in clubhead speeds across levels of shaft stiffness.
Based on the previous arguments it should not be inferred that certain levels of
shaft stiffness cannot outperform others for a particular swing when considering
increased driving yardage. Rather it should be understood that if driving distance was
found to be meaningfully different across levels of shaft stiffness, then that increased
driving yardage would be a result of factors other then differences in ball speed. These
other factors, namely, ball launch angle and ball spin rate are influenced by clubhead